First-principles approach to excitons in time-resolved and angle-resolved photoemission spectra

TL;DR

This paper introduces a first-principles diagrammatic approach to accurately capture excitonic features in time-resolved photoemission spectra, overcoming limitations of traditional GW approximations.

Contribution

The work develops a novel ab initio method using excited Green's functions to include excitonic effects in TR photoemission, with detailed derivations and application to a model system.

Findings

Excitonic features are not captured by standard GW approximations.

The proposed method accurately describes excitons in time-resolved spectra.

Exciton dispersion can be observed in TR and angle-resolved photoemission.

Abstract

We show that any {\em quasi-particle} or GW approximation to the self-energy does not capture excitonic features in time-resolved (TR) photoemission spectroscopy. In this work we put forward a first-principles approach and propose a feasible diagrammatic approximation to solve this problem. We also derive an alternative formula for the TR photocurrent which involves a single time-integral of the lesser Green's function. The diagrammatic approximation applies to the {\em relaxed} regime characterized by the presence of quasi-stationary excitons and vanishing polarization. The main distinctive feature of the theory is that the diagrams must be evaluated using {\em excited} Green's functions. As this is not standard the analytic derivation is presented in detail. The final result is an expression for the lesser Green's function in terms of quantities that can all be calculated {\em ab initio}. The validity of the proposed theory is illustrated in a one-dimensional model system with a direct gap. We discuss possible scenarios and highlight some universal features of the exciton peaks. Our results indicate that the exciton dispersion can be observed in TR {\em and} angle-resolved photoemission.